Unified Scattering Parameters formalism in terms of Coupled-Mode Theory for investigating hybrid single-mode/two-mode photonic interconnects

Hybrid single-mode/multimode optical interconnects tend to become all-pervading in Photonic Integrated Circuits (PIC) involving Modal Division Multiplexing (MDM), where information is distributed over different spatial modes... [ view full abstract ]

Hybrid single-mode/multimode optical interconnects tend to become all-pervading in Photonic Integrated Circuits (PIC) involving Modal Division Multiplexing (MDM), where information is distributed over different spatial modes sharing the same wavelength. Mode add-drop multiplexing is typically achieved by means of asymmetric directional couplers between single and multimode waveguides, whose dimensions are designed in order to enable an index-matching condition between the modes to be coupled.
In terms of Coupled-Mode Theory (CMT), each mode-to-mode coupling is described by two quantities: a detuning (or mismatch between the propagation constants in the k-space) and a coupling constant (whose physical origin lies in evanescent tunneling), both rendered dimensionless by way of spatial integration over the total interaction length.
We apply this formalism to characterize a typical ring-based mode multiplexer (see Figure). For the sake of clarity, we consider only the TE state of polarization. This structure consists of a narrow access waveguide and a micro-ring racetrack resonator, both designed to guide only the fundamental TE0 mode. A second coupled waveguide (bus) is dimensioned to support both its TE0 and TE1 modes. Waveguide widths can be arranged so that the effective index of the TE0 mode of the narrow waveguide matches that of the TE1 mode of the wide (bus) one, thus ensuring a high coupling efficiency. Importantly, the presence of the micro-ring limits the modal power conversion only to signal tuned on its resonant wavelengths.
The key feature of our approach is the way we treat the two-mode output waveguide as formally equivalent to a set of two identical, mutually coupled single-mode waveguides (which amounts to a mere change of basis, as far as the even/odd modes of the two-mode waveguide are concerned). The simultaneous co-directional interaction between the three scalar waves is solved analytically as a function of the mismatch and the coupling constants. As a result, we obtain a closed-form expression of the scattering parameters relating the single-mode input to the even- or odd-mode output.
This approach can prove of interest for the systematic investigation of short-range optical interconnects, notably in terms of tolerances to technological or geometrical parameters.